Question

One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 5 or a Club. Note that the ace is considered a low card.The probability that the card selected is less than 5 or a club is.(Type an integer or a simplified fraction.)

Answer 1

The total number of cards in a deck of cards is: 52

The total number of club cards is: 13

The total number of cards that less than 5 is: 8.

The probability of selecting a club card is,

`\begin{gathered} P(Club)=\frac{Total\text{ number of club cards}}{\text{Total number of cards}} \\ =(13)/(52) \\ =(1)/(4) \end{gathered}`

The probability of selecting a card that is less than five is,

`\begin{gathered} P(card<5)=(8)/(52) \\ =(2)/(13) \end{gathered}`

The total number of club card that is less than 5 is 3.

The probability of selecting a club card and a card that is less than 5 is,

`P\text{ (club and less than 5)}=(3)/(52)`

The probability of selecting a card that is a club or less than 5 is,

`\begin{gathered} P\text{ (Club or less than5)}=P(Club)+P\text{(card less than 5)-P(Club and less than 5)} \\ =(1)/(4)+(2)/(13)-(3)/(52) \\ =(21)/(52)-(3)/(52) \\ =(9)/(26) \end{gathered}`

Thus, the probability of selecting a club card or card that is less than 5 is 9/26.